question

I think the 6/3 would cover it. 120V at 50A is going to be 6000 watts. At that wattage, the duration won’t be long enough to stress the cabling.

The spec sheet for the 120/3000 Multi indicates 6 AWG is the largest wire size it can accommodate for the AC inputs and outputs.

While the transfer switch is rated at 50 amps and you can theoretically get 25 more amps out of the inverter totaling 75 amps I would not design a system based on that maximum to a single output from the Multi. The input to the Multi may disconnect for a number of reasons leaving you with only the inverter's output at least for a while. This could quickly cause an overload and shutdown the inverter. For this reason, I would not design a system with more than 25 amps load on AC 1 output. Additional loads totaling 50 amps could be connected to AC 2 output. These are shed when the AC input drops out so there's significantly less chance of inverter overload. There is still a potential for overload with AC input present but the inverter off. This condition would trip the 50 amp input breaker. To avoid tripping the input breaker, the total of all loads should probably be less than 50 amps, so 25 amps max on AC 1 out and the remainder on AC 2 out.

This approach also reduces current in the AC output conductors. AC 1 out could use 10 AWG wire (30 amps max at 60 C). AC 1 out could use 6 AWG (55 amps max at 60 C).

If you are worried about ampacity, use 6AWG boat cable rated BC-5W2. 6AWG is rated for 120A in single wire runs, or 84A in 3 wire bundles. Most quality marine wire has this rating.